Before I answer - whatever you do, get laser safety glasses appropriate for what you are thinking of getting.
Your first question is fairly simple, though double edged - There's not a lot of difference between colours in actual burning capability, but there is a huge difference between what is powerful and available at different colours (wavelengths).
For example, 445nm (blue) lasers are readily avaliable and can output a lot of power (1-7W), you won't find a green diode that can output more than 1W. Much more important for burning is focus - i.e. even a relatively low-power laser (e.g. 100mw) can burn some materials if focused to a narrow point.
Your second question on the other hand slightly worries me. Never use powerful lasers (class 2 or higher, i.e.) indoors without proper laser safey glasses. You should not entertain the fact of going blind - 100mw of Red and 100mw of Green will cause the same damage to a retina (unless the green is an IR unfiltered 532nm, in which case there is likely much more power being output in the invisible part of the spectrum)
As far as burning things with a laser the color of the material to be burned is also a factor. Black objects absorb more of the beam's power than light colors or white. If you are using a red laser, you don't want to try to burn a red material as it will reflect more light than it will absorb.
Power density of your beam is also an issue here. Single mode diodes like the S06J and the BDR-209, 405nm lasers, have higher power densities than many higher power multi mode diodes do.
The wording of your last question is cause for concern. It sounds like you are looking for the laser that will blind the best. Always take laser safety very seriously. It is the power density of the beam, not the color that will cause the worst retina burns. Color doesn't matter at all. Get the appropriate laser eye wear for the laser you intend to buy.
A laser beam has no temperature - there is no inherent "temperature" to a laser beam.
Heat is the random motion of matter particles (atomic or molecular particles).
A laser beam itself is not made of matter but of photons, which have no mass, thus a laser beam can have no temperature.
"Heat" is caused by a laser beams energy being absorbed by a materials surface and turning light energy into heat energy.
"Burning": depends upon the ability of the target to absorb and convert the light energy of whatever wavelength to heat.
As others have already stated. Its not the 'colour' that is better at burning. Wavelength is somewhat important, but only due to the materials absorption. As Encap has stated well, lasers do not carry thermal energy. Instead it goes on several factors. Power density, being a big one.
405nm is your best but for raw power 445 is your best choice. As others have said, be careful. You should consider these lasers as weapons because you will blind someone. It's not a maybe but 100 percent certainty that you will blind yourself or someone if hit in the eye. Remember it's a loaded gun.
I'd agree that the shorter wavelengths have the most burning potential, even fluorescence causes heating of the target and potentially setting it on fire. If you want to focus your beam down to a small spot to get the maximum power density possible a single mode diode would be the best choice, which results in 405 nm.
You can get a lot more raw power from multimode diodes like the 445's though, so it would depend on what you actually would like to burn with your laser.